Multiobjective programming under d-invexity

Efficiency and Duality in Nondifferentiable Multiobjective Programming Involving Directional Derivative

“…Antczak [14] studied d-invexity is one of the generalization of invex function, which is introduced by [15]. In [14], Antczak established, under weaker assumptions than Ye, the Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions for weak Pareto optimality and duality results which have been stated in terms of the right differentials of functions involved in the considered multiobjective programming problem.…”

“…corrrected the Karush-Kuhn-Tucker necessary conditions in [14] and discussed the sufficiency and duality under d r   type I functions. Recently, Silmani and Radjef [20] introduced generalzed d I -invexity in which each component of the objective and constraint functions is directionally differentiable in its own direction and established the necessary and sufficient conditions for efficient and properly efficient solutions.…”

Sufficiency and Duality in Nonsmooth Multiobjective Programming Problem under Generalized Univex Functions

“…Also, hypotheses (i), (ii), and (iv) of Theorem 18 are clearly satisfied and it follows that is an efficient solution of the above defined multiobjective optimization problem, whereas it will be impossible to apply for this purpose the sufficient optimality conditions given in Kharbanda et al [18], Ahmad [17], Slimani and Radjef [12], Mishra and Noor [10], Mishra et al [16], Antczak [9], Suneja and Srivastava [19], and Ye [8]. …”

“…Also, he derived necessary and sufficient optimality conditions taking functions ( ; ) and ( ; ) to be convex. However, Antczak [9] considered the directional derivatives of objective and constraint functions to be preinvex and derived duality results for Wolfe type, MondWeir type, and mixed type dual programs. Mishra and Noor [10] extended the class of functions to --type I functions and obtained sufficient optimality and duality results for Mond-Weir type multiobjective dual program.…”

“…In this paper, we introduce a new generalized class of ( , , , )--V-type I univex functions which generalizes the class of functions introduced by Kharbanda et al [18], Ahmad [17], Slimani and Radjef [12], Mishra and Noor [10], Mishra et al [16], Antczak [9], Suneja and Srivastava [19], and Ye [8]. Further, we establish weak, strong, converse, and strict converse duality results for Mond-Weir type multiobjective dual program.…”